2.5-D modeling of seismic wave propagation; boundary condition, stability criterion, and efficiency

The modeling of 3-D wave propagation in media having only 2-D variation in the elastic properties--so-called 2.5-D modeling--is achieved using the wavenumber transform, in which multiple 2-D problems are solved, each one associated with a different strike-direction wavenumber (k y ). We derived a 2.5-D transmitting boundary condition in the frequency domain, which has no simple representation in the time domain. It yields significantly improved results over existing boundary conditions. For time-domain methods, attenuating boundary conditions must be applied. The 2.5-D stability criterion changes from the 2-D to the 3-D criterion as the wavenumber increases from zero to the maximum value for traveling waves, respectively. In the frequency-wavenumber (omega -k y ) domain at a given spatial location, the wavefield for a fixed frequency (omega ) oscillates at progressively higher rates as wavenumber (k y ) increases from zero to the maximum value for traveling waves. A nonuniform sampling scheme in wavenumber space, to exploit the oscillatory nature of the wavefield, yields significant efficiency improvement over the normal uniform sampling scheme.